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Volume of a Triangular Prism Calculator

Enter the triangle’s base and height plus the prism’s length, and get the volume instantly — the cross-section area (½bh) times the length, with steps shown.

Example: with Triangle base (b) 6 · Triangle height (h) 4 · Prism length (L) 10 · Units inches (in) → Prism volume: 120.00 in³.

Computed by the calculator below using its default values. Change any input to see your own numbers.

Prism volume
Also equals
Triangle area (½bh)
Steps

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Volume of a triangular prism formula

A triangular prism is a triangle stretched along a length, so its volume is the triangle’s area times that length: V = ½ × b × h × L. With the defaults — base 6 in, height 4 in, length 10 in — the cross-section is ½ × 6 × 4 = 12 in², and 12 × 10 = 120 in³.

Searches for the “volume of a triangle” almost always mean this shape: a triangle is flat and has area only, but give it a length — a tent, a ramp, a Toblerone box — and it becomes a prism with volume. The formula works for any triangle type as long as h is the perpendicular height to the base you chose. Know only the three sides? Get the area from Heron’s formula first: a 3-4-5 triangle has area 6, so a 10-unit-long prism on it holds 60 cubic units.

How it’s calculated

Volume = ½ × b × h × L: the triangular cross-section area (½ × base × perpendicular height) multiplied by the prism’s length. Conversions: 1 US gallon = 231 in³ exactly, 1 ft³ = 7.48052 gal (NIST Handbook 44), 1 liter = 1,000 cm³, 1 m³ = 1,000 L.

Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.

Common mistakes

  • Forgetting the ½ — b × h × L is the volume of a rectangular box, twice the prism’s.
  • Using a slanted side of the triangle as its height — h must meet the base at 90°.
  • Mixing units, like a base in inches with a length in feet — convert to one unit first.

Frequently asked questions

What is the volume of a triangular prism formula?

V = ½ × b × h × L, where b and h are the triangle’s base and perpendicular height and L is the prism’s length. It’s simply cross-section area × length.

How do I find the volume of a triangular prism from three sides?

Use Heron’s formula for the triangle’s area, then multiply by the length. Sides 3, 4, 5 give area 6 (s = 6; √(6×3×2×1) = 6), so a length of 10 makes the volume 60.

Can you find the volume of a triangle?

Not literally — a triangle is a flat 2D shape with area ½bh, not volume. What people usually want is the volume of a triangular prism, which is that area times the prism’s length.

Which measurement is the height?

The triangle’s own height — the perpendicular distance from the chosen base to the opposite corner. The distance between the two triangular ends is the length L, a separate input.